Abstract

A set of n times n Boolean matrices along with the Boolean matrix multiplication operation form a semigroup. For each matrix A it is possible to find index mu and period łambda, such that A mu = A mu + łambda, and mu, łambda are the smallest positive integers with this property. We are concerned with a question: How many n times n Boolean matrices have the given index, and period? A new algorithm is presented that was used to compute index and period statistics of all square Boolean matrices up to n=8. Computed statistics are presented in the appendix of the paper.

Keywords

Cite this article

@article{cai-110155,
  author  = {Pavol Zajac and Matuš Jókay},
  title   = {Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8},
  journal = {Computing and Informatics},
  volume  = {31},
  number  = {6},
  pages   = {1329--1344},
  year    = {2012},
  issn    = {1335-9150},
  url     = {https://cai.type.sk/content/2012/6/computing-indexes-and-periods-of-all-boolean-matrices-up-to-dimension-n-8/}
}
Download .bib